ABSTRACT
In the same paper [41] he gives some necessary and some sufficient conditions for existence of a mapping from 2X or from C(X) onto X.
Since the hyperspace Fi(X) of singletons of X is a subspace of 2X and is homeomorphic to X, the continuum X can be considered as naturally embedded in C(X). Thus, if we identify X with Fi(X), we have X C C(X) C 2X. So, the following is a particular case of Problem 1.1 (see [40, p. 413] and also [43, (6.2), p. 270]).
